Problem: Multiply the following complex numbers, marked as blue dots on the graph: $[6(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))] \cdot [1]$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $6(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))$ ) has angle $\frac{3}{4}\pi$ and radius $6$ The second number ( $1$ ) has angle $0$ and radius $1$ The radius of the result will be $6 \cdot 1$ , which is $6$ The angle of the result is $\frac{3}{4}\pi + 0 = \frac{3}{4}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{3}{4}\pi$.